Helga Hunter, 68, from Angus says she had not even considered the issue until receiving a letter from Angus South MSP Graeme Dey saying she was welcome to stay in post-Brexit Scotland.
She and her Scottish husband Michael have lived in Arbroath, Angus, for more than 20 years after meeting in the former West Germany.
Scottish Conservative constitution spokesman Adam Tomkins accused the SNP of “firing out scaremongering letters.”
He added: “It is using these tactics to stoke up fear among people who have no question marks over their status.
“It’s a shameful approach. The SNP should stop point-scoring and try being more constructive as we enter a tricky negotiation phase.”
The letter to Mrs Hunter, on Scottish Parliament- headed paper, sought to reassure her that she “and her family” were welcome to remain in Scotland.
Mr Dey adds: “While there will be no immediate changes in your circumstances I appreciate there remains great uncertainty over how events will unfold.”
But Mrs Hunter said she had never given her domestic status “a second thought since the day we got married”.
She said: “I never had any worries until I received this letter – I didn’t know what to think because it says there will be no ‘immediate changes’. I thought, ‘What are they going to do?’ I’ve paid my taxes here and never lived off the government – I always worked.
“I love it in Scotland and always felt very welcome, but this obviously casts doubt in my mind over the future.
The SNP said letters are going out across Scotland and stated that the blanket letter is “the right approach to take” in an “increasingly hostile atmosphere” following the UK vote to leave the EU.
An SNP spokesman said: “Graeme Dey and other SNP parliamentarians have rightly taken the lead in engaging with EU citizens in their constituencies and ensuring them that they remain welcome in Scotland and their contribution is valued.”